Not letting other browsers use their own JS engine (which is what it means to 'forcing them to use Internet Explorer engine on Windows' in your analogy) is beca

Not letting other browsers use their own JS engine (which is what it means to 'forcing them to use Internet Explorer engine on Windows' in your analogy) is because Apple want to disallow write|execute for people's safety. Perhaps you're right. Maybe it's entirely coincidental that Apple's policy also prevents owners of Apple devices from using a browser with modern features that would allow web apps to effectively compete with the native apps from which Apple gets a huge cut of the revenue because of its monopoly control over the app store.